Groundwater flow in a medium with a parquet-type conductivity distribution

Steady and periodic Darcian ground water flows in an aquifer, in which conductivity changes periodically in space, is studied. The parquet is composed of a doubly periodic system of ‘black’ and ‘white’ rectangles such that two adjacent rectangles constitute an elementary cell. The rigorous conjugation conditions (head and normal flux continuity along two adjacent rectangles) are satisfied along the medium division boundary and the periodicity conditions hold along the cell boundary such that within the cell the flow is two-dimensional. Explicit rigorous expressions for the specific discharge vector are presented. The effective conductivity is calculated by rigorous integration of the head and velocity fields over the elementary cell. With variation of the angle of the imposed field the absolute value of effective conductivity is shown to be an ellipse. A steady state regime and a cyclostationary flow are analyzed by tracking marked particles on the scale of the elementary cell. The kinematic characteristics (travel time distributions, path lines, and distortion pictures of reference volumes) are calculated using the Runge–Kutta integration for a limiting case when one side of the constituting rectangles tend to infinity (a fault in a standard layered system).